Factoring the Sum and Difference of Cubes

In mathematics, factoring is one important topic in algebra. Factoring the sum and difference of cubes are the one special case of polynomials in factoring.. Factoring is the
process of performing the operation of arithmetic multiplication in reverse. Let us solve some example problems for factoring the sum and difference of cubes.

Factoring the Sum and Difference of Cubes:

Sum of cubes:

(a3 + b3) = (a + b) (a2 - ab + b2)

Differences of cubes:

(a3 – b3) = (a – b) (a2 + ab + b2)

Example Problems for Factoring the Sum and Difference of Cubes:

Different example problems for factoring the sum and difference of cubes are,

Problem 1:

Factor the given polynomial expression

8x3 – 64

Solution:

Given polynomial expression

8x3 – 64

It is in the form of difference of cubes, because the expression is in the form

(2x)3 – (4)3

Factor the expression

The first term of the expression can be written as

8x3 = 2x . (2x)2

The last term of the expression can be written as

64 = 4 . 42

Now we factor the given expression

(a3 – b3) = (a – b) (a2 + ab + b2)

In the given expression,

a = 2x and b = 4

8x3 – 64 = (2x -4) (4x2 + 2x (4) + 42)

=(2x – 4)(4x2 + 8x +
16)

Answer:

8x3 – 64 =(2x – 4) (4x2 + 8x + 16)

Problem 2:

Factor the given polynomial expression

64m3 – 1000

Solution:

Given polynomial expression

64m3 – 1000

It is in the form of difference of cubes, because the expression is in the form